Geodesic
A CONTINUOUS INTERPOLATION BETWEEN CONSERVATIVE AND DISSIPATIVE SOLUTIONS FOR THE TWO-COMPONENT CAMASSA–HOLM SYSTEM
Forum of Mathematics, Sigma, Tome 3 (2015)

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We introduce a novel solution concept, denoted ${\it\alpha}$-dissipative solutions, that provides a continuous interpolation between conservative and dissipative solutions of the Cauchy problem for the two-component Camassa–Holm system on the line with vanishing asymptotics. All the ${\it\alpha}$-dissipative solutions are global weak solutions of the same equation in Eulerian coordinates, yet they exhibit rather distinct behavior at wave breaking. The solutions are constructed after a transformation into Lagrangian variables, where the solution is carefully modified at wave breaking. 
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     author = {KATRIN GRUNERT and HELGE HOLDEN and XAVIER RAYNAUD},
     title = {A {CONTINUOUS} {INTERPOLATION} {BETWEEN} {CONSERVATIVE} {AND} {DISSIPATIVE} {SOLUTIONS} {FOR} {THE} {TWO-COMPONENT} {CAMASSA{\textendash}HOLM} {SYSTEM}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
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     doi = {10.1017/fms.2014.29},
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KATRIN GRUNERT; HELGE HOLDEN; XAVIER RAYNAUD. A CONTINUOUS INTERPOLATION BETWEEN CONSERVATIVE AND DISSIPATIVE SOLUTIONS FOR THE TWO-COMPONENT CAMASSA–HOLM SYSTEM. Forum of Mathematics, Sigma, Tome 3 (2015). doi: 10.1017/fms.2014.29

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